Sunday, February 28, 2016

Higgs inflation

The case for inflation is extremely strong. If you don't already understand how strong the case is, then I suggest watching the following lecture at MIT by Alan Guth. Alan Guth is the originator of the concept of inflation, and now he provides a fairly unbiased judge of the theory, since his original model for inflation has been effectively disproven (i.e. quantum tunneling from the false vacuum through a barrier to the real vacuum.)
The main evidence for inflation are the following:
(1) Horizon problem:  the universe that we see is extremely similar even though there was no way for parts of the universe that we see today to have been in contact...unless the universe we see today came ultimately from a small region that had been in contact, and then got inflated to a much larger size.
 (2) Flatness problem:  Overall, there is virtually no curvature (k) in the universe. In a matter dominated universe, the overall curvature grows with time, so this means that the curvature when the temperature was >TeV must have been extremely small. The smallness of the curvature can be explained if our universe went through a period of inflation before the temperature dropped to ~TeV.
(3) Small, Adiabatic, Gaussian fluctuations in curvature: While the overall curvature of the universe is small or zero, there are local fluctuations in the curvature that end up canceling overall, i.e. while the curvature might be negative in some locations, it is positive in other locations so that the overall curvature is near zero. (Imagine living on a fixed point in Sahara desert and imagine that the farthest that you can see is 100 km in any direction. You would see local variations in the curvature, due to dune piles scattered throughout the desert. However, the overall curvature would be virtually zero. In other words, you would be forced to conclude that, if you did live on the surface of a sphere, then the radius of the sphere is much, much greater than 100 km.) In this analogy, the dune piles are the remnants of the initial fluctuations before inflation. The primordial fluctuations are random, uncorrelated, adiabatic and overall add-up to near-zero curvature.

These are the three main sources of evidence for inflation.
What's interesting is that the standard model of physics provides a natural candidate for the inflation field: the Higgs field. Like the inflation field, the Higgs field is a scalar field, in the sense that at every point in 4-D space-time, there is a value (a quaternion) for the Higgs field. Examples of day-to-day scalar fields are pressure/temperature/electric potential. These should be contrasted with a vector field, which has at every point in space-time both a magnitude and a direction. Examples of day-to-day vector fields are electric field, magnetic field, and wind velocity. At every point, the vector field has both a magnitude and a direction.

The Higgs field is a fundamental scalar field. Scientists are still working out the shape of the Higgs energy density as a function of the value of the Higgs fields. We /they know that the shape of the energy density vs. field value when the value of the field is close to the value of the field (v = 246 GeV) which is a local (and perhaps global) minimum in the energy density. (see inset in the figure below from the paper by Bezrukov and Shaposhnikov.) What is still uncertain is the shape of the curve far from v = 246 GeV. It is well known that the coupling of the Higgs field to particles (such as the top quark) causes the shape of the curve to look somewhat like the curve below. Depending on the coupling to the top quark and the self-coupling of the Higgs field, the potential can look like the one below, which goes to an asymptote. The potential below is also nearly exactly the shape of the potential needed to explain slow-roll inflation. It is called slow-roll because of the small gradient in the field at large values of the Higgs field.

 Figure#1: Higgs energy density versus field value from the paper by Bezrukov and Shaposhnikov
 titled " The Standard Model Higgs boson as a the inflaton."
 Interestingly, the shape of the Higgs field in the case listed above is nearly the same as the primordial potential field that is measured experimentally. (By experimentally, I mean when combining data from WMAP/Planck/ACT/SPT/WeakLensing/LymanAlphaForest.) The primordial potential field was estimated by Hunt and Sarkar using the data list above and can be seen below:

Figure#2: Primordial potential of the inflaton field as estimated by Hunt and Sarkar

 Below, I show the data from Hunt and Sarkar, but with the Higgs potential field imposed on top.

 Figure#3: Primordial potential of the inflaton field as estimated by Hunt and Sarkar
with the Higgs field estimated by Bezrukov and Shaposhnikov imposed on top as a black line. (In the case that the Higgs self-coupling and the coupling between the Higgs field and the top quark produce an asymptotic value for the potential field.)

What one can see in Figure#3 is that the experimental data for the primordial inflaton field can be well described so far by a Higgs-like scalar field. Also interesting is that the potential field takes a nose-dive at smaller and smaller scales. This nose-dive in power help to explain why there appears to be a lack of fluctuations at the scale of galaxies (i.e. 1-100 kpc.) (Perhaps, we don't need warm dark matter as a complete explanation for the lack of fluctuations at small scale???)

Because the shape and size of the Higgs scalar field is so nearly the same as the shape and size of the inflaton field required to create primordial fluctuation, it is my opinion the Higgs field is the inflaton field. To prove this conjecture will require further research by theorists into the exact shape of the Higgs field and further experimental data on the mass of the top quark and Higgs boson as well as experimental data on the primordial fluctuations at both large and small scales (the middle scale seems pretty much nailed down.) Theorists will need to calculate the running of the Higgs field at large energy scales by including more than 5 loops of self-coupling and coupling to bosons/fermions.

All-in-all, it appears that the Higgs field is the inflaton field and there is no need to have supersymemtric particles to save the Higgs from going unstable.(Hence, another reason why I think that Supersymemtry is dead!)


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